不确定参数下群体博弈均衡的存在性与通有稳定性  

Existence and Generic Stability of Equilibria for Population Games with Uncertain Parameters

作　　者：赵薇 杨辉 吴隽永 ZHAO WEI;YANG HUI;WU JUANYONG(School of Mathematics and Statistics,Guizhou University,Guiyang 550025)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《应用数学学报》2020年第4期627-638,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11271098,11861020,11761023);贵州省科技厅自然科学基金(黔科合LH字[2016]7424,7425号)资助项目.

摘　　要：本文在已知不确定参数变化范围的假设下,研究了不确定参数下群体博弈均衡的存在性与通有稳定性.首先,基于经典非合作博弈NS均衡概念提出了不确定参数下群体博弈NS均衡的定义;其次,在支付函数连续性与凸性的一定假设下,利用Ky Fan不等式证明了均衡的存在性;最后,给出了不确定参数下群体博弈模型NS均衡集通有稳定性的相关结论,运用Fort引理证明了在Baire分类的意义下,当支付函数发生扰动时,大多数不确定参数下群体博弈的NS均衡点集都是稳定的.Under the assumption that the range of varying uncertain parameters is known,the existence and generic stability of equilibria for population games with uncertain parameters are investigated in this paper.First,on the basis of NS equilibria in classical noncooperative games,the notion of NS equilibria for population games with uncertain parameters is defined.Second,with some hypotheses about the continuity and convexity of payoff functions,the existence theorem of NS equilibrium points for population games is also proved by means of Ky Fan inequality.Finally,some related results are obtained about the generic stability of NS equilibrium points for population games with uncertain parameters.By employing Fort lemma,we prove that,in the sense of Baire category,most of the NS equilibrium point sets for population games with uncertain parameters are stable when the payoff functions are perturbed.

关 键 词：群体博弈 不确定参数 NS均衡 存在性 通有稳定性 

分 类 号：O177.91[理学—数学]